Topology Unit
In mathematics, topology is the study of the properties of space that are preserved under the continuous deformations, such as stretching, twisting, crumpling, and bending, but not tearing or gluing. For this reason, topology is often referred to as “the rubber sheet geometry”.
Topology developed as a field of study out of geometry and set theory, through the analysis of concepts such as space, dimension, and transformation. Leonhard Euler’s Seven Bridges of Königsberg Problem and the Euler Characteristic are arguably the field’s first theorems. 
Johann Benedict Listing introduced the term topology in the 19th century, although it was not until the first decades of the 20th century that the idea of a topological space was developed. By the middle of the 20th century, topology had become a major branch of mathematics.
One of the most famous shapes in topology is a Möbius strip, named after the German mathematician August Ferdinand Möbius. In one of those strange quirks of mathematical fate, Möbius was not actually the first to discover or describe the object. Credit should go to Johann Benedict Listing. Working independently, Listing first encountered the surface in July 1858. He published his discovery in an 1861 paper devoted to generalizations of Euler’s formulas for polyhedra.

Lecture Notes & Other Resources
TENTATIVE SCHEDULE FOR THE UNIT
Topology Reading
Subfields of Topology
VIDEO: Introduction to Topology
Topology  Day 1
Topology vs Geometry
Classifications of Objects
Watch an Animation of a Doughnut morphing into a Coffee Cup.
Because both a doughnut and a coffee cup have one hole (handle), they can be mathematically, or topologically, transformed into one another without cutting them in any way. For this reason, it has often been joked that topologists cannot tell the difference between a coffee cup and a doughnut.
Topology  Day 2
What is a Möebius Strip?
VIDEO CLIP: In the movie "Avengers End Game (2019)", there is a nice scene about the Möebius strip.
VIDEO CLIP: In the cartoon "Futurama", there is a race on a Möebius strip and they use the word "topology".
VIDEO: What is a Klein Bottle?
VIDEO: Forming a Klein Bottle?
VIDEO: What if the Universe were Shaped like a Dough?
VIDEO: 1979 Atari Asteriods Arcade Game Play
Introduction to the Torus WS
Topology  Day 3
Brussel Sprouts, the Euler Characteristic, and Planar Graphs
VIDEO: Brussel Sprouts Explained Mathematically
The Online Game of Planarity
Topology  Day 4
The Game of Sprouts
Topology  Day 5
Map Coloring
VIDEO: The Four Color Map Theorem
Map Coloring Challenge
Jordan Curves
Topology Unit ASSESSMENT
Topology Reading
Subfields of Topology
VIDEO: Introduction to Topology
Topology  Day 1
Topology vs Geometry
Classifications of Objects
Watch an Animation of a Doughnut morphing into a Coffee Cup.
Because both a doughnut and a coffee cup have one hole (handle), they can be mathematically, or topologically, transformed into one another without cutting them in any way. For this reason, it has often been joked that topologists cannot tell the difference between a coffee cup and a doughnut.
Topology  Day 2
What is a Möebius Strip?
VIDEO CLIP: In the movie "Avengers End Game (2019)", there is a nice scene about the Möebius strip.
VIDEO CLIP: In the cartoon "Futurama", there is a race on a Möebius strip and they use the word "topology".
VIDEO: What is a Klein Bottle?
VIDEO: Forming a Klein Bottle?
VIDEO: What if the Universe were Shaped like a Dough?
VIDEO: 1979 Atari Asteriods Arcade Game Play
Introduction to the Torus WS
Topology  Day 3
Brussel Sprouts, the Euler Characteristic, and Planar Graphs
VIDEO: Brussel Sprouts Explained Mathematically
The Online Game of Planarity
Topology  Day 4
The Game of Sprouts
Topology  Day 5
Map Coloring
VIDEO: The Four Color Map Theorem
Map Coloring Challenge
Jordan Curves
Topology Unit ASSESSMENT

